Since Miiduu.com has been listed with Google for a long time, when you search your store name in Google, the miiduu.com site may come first because of its visibility and popularity.
 
If you are store owner using own domain and you're concerned that your own domain url doesn’t come first in Google search, you may do follow things to solve the issue.
 

1. Increase your visibility by submitting and optimizing your website for Google search at http://www.google.com/submityourcontent/.
This will help Google to record your own domain url. 

2. Verify your site on Google Webmaster. For detailed information, click on http://help.miiduu.com/customer/portal/articles/1617379-miiduu-|-how-to-verify-your-site-on-google-webmaster?b_id=4195

3. Make your store more SEO friendly with these ideas.  http://help.miiduu.com/customer/portal/articles/1617390-miiduu-|-how-to-make-your-store-more-seo-friendly?b_id=4195 
 
These steps will be helpful in increasing the visibility of your own domain, and should help improve your search engine rank in Google. But please note that the search results are controlled by Google. To get the detailed information about ranking rules, please see related Google FAQ.